I wasn't really making a puzzle, but conjecturing out loud.

Though, you should make that into a puzzle.

Edit: The reasoning I'm thinking out loud is because every strictly increasing monotonic sequence of natural numbers has an associated real number attached to it ([Beatty sequences](https://en.wikipedia.org/wiki/Beatty_sequence#)).

It would, therefore, stand to reason that if every such sequence also has a graph, that we could then associate to each graph the real number that's associated to each sequence.